Identify the relationship in a number pair - CogAT Grades K 2

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Why Do We Look for Patterns in Numbers?

People have loved finding patterns in numbers for a very long time! Long ago, people counted things like sheep and apples. They noticed that numbers are connected to each other. For example, if you have 2 apples and get 3 more, you always end up with 5. That is a pattern!

Long Ago • Counting Begins

People used fingers and stones to count animals and food. They saw that numbers follow a set order.

Ancient Times • Finding Rules

People noticed that adding 1 always gives the next number. This was one of the first number rules!

In School • Number Pairs Today

Today, you learn to find the hidden rule between two numbers. This helps you think like a math detective!

When you see two numbers together, there is often a secret rule that connects them. Your job is to figure out that rule. This is what identifying the relationship in a number pair means. Let's learn how!

SECTION 2

What Is a Number Pair Relationship?

A number pair is just two numbers that go together. The relationship is the rule that shows how the first number turns into the second number. Think of it like a magic machine: you put one number in, and the machine does something to it, and a new number comes out!

Adding

The second number is bigger. Something was added! Example: 3 → 5 means add 2.

Subtracting

The second number is smaller. Something was taken away! Example: 7 → 4 means subtract 3.

Same Rule Every Time

The secret rule works the same way for every number pair in a group. If the rule is add 2, it is always add 2.

Check Your Work

Always try your rule on every pair to make sure it works. If it does not fit, try a different rule!

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KEY TAKEAWAY

Think of a number pair like a recipe. If you always add 2 cups of sugar to your bowl, every bowl gets 2 more cups. The rule stays the same every time, just like the recipe!

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See the Number Pair Machine

This diagram shows a Number Pair Machine. A number goes IN on the left. The machine uses a secret rule (add 3). The new number comes OUT on the right. Notice the rule is the same every time!

Look at the picture above. The purple box on the left is the first number. The blue box on the right is the second number. The machine in the middle shows the secret rule. Every time, the machine adds 3. So the pair (2, 5) means 2 + 3 = 5. The pair (4, 7) means 4 + 3 = 7. The rule is always "add 3."

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How to Find the Rule

Here are the steps to find the secret rule between two numbers. Follow these steps like a detective following clues!

ADDING RULE

First Number + ? = Second Number

If the second number is bigger, something was added. Count up from the first number to the second number to find what was added.

SUBTRACTING RULE

First Number − ? = Second Number

If the second number is smaller, something was taken away. Count down from the first number to the second number to find what was subtracted.

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Detective Tip!

Always ask yourself: "Did the number get bigger or smaller?" If it got bigger, think about adding. If it got smaller, think about subtracting.

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Different Kinds of Number Pair Rules

Number pairs can follow different kinds of rules. Let's look at the most common ones you will see on the CogAT test. Each rule is like a different type of magic machine!

This chart shows four types of rules: add, subtract, double, and stay the same. Each box shows two examples of the same rule.

Look at the four boxes above. The green box shows an add rule where we add 2 each time. The pink box shows a subtract rule where we take away 3 each time. The yellow box shows a doubling rule where the number gets twice as big. The purple box shows a rule where the number stays the same.

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Let's Solve One Together!

Here is a problem just like the ones on the CogAT test. Let's solve it step by step!

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The Problem

Look at these number pairs: (1, 4) and (3, 6). What is the rule? If the rule keeps going, what number goes with 5? That means: (5, ?).

Step-by-Step Solution

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Step 1 — Look at the First Pair

The first pair is (1, 4). The first number is 1. The second number is 4. Is 4 bigger or smaller than 1? It is bigger! So something was added.

The second number is bigger, so we are adding.
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Step 2 — Find How Much Was Added

Count up from 1 to 4. You go: 1… 2… 3… 4. That is 3 jumps. So the rule might be add 3. But we need to check with the next pair!

1 + 3 = 4 ✓
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Step 3 — Check with the Second Pair

The second pair is (3, 6). If the rule is add 3, then 3 + 3 should equal 6. Let's check: 3 + 3 = 6. Yes! The rule works!

3 + 3 = 6 ✓ — The rule is confirmed: add 3.
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Step 4 — Use the Rule to Find the Answer

Now use the rule on 5. The rule is add 3. So 5 + 3 = 8. The missing number is 8!

5 + 3 = 8. The answer is (5, 8).

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Helpful Tips and Common Mistakes

Good Strategy	Common Mistake
Check the rule on every pair to make sure it works.	Only looking at one pair and guessing the rule.
Ask: Did the number get bigger or smaller?	Forgetting to compare the two numbers.
Use counting or fingers to find the difference.	Trying to guess without counting.
Try adding first. If that doesn't work, try subtracting.	Mixing up adding and subtracting.

Good strategies vs. common mistakes

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KEY TAKEAWAY

Finding a number pair rule is like being a detective. You look at the clues (the number pairs), you guess the rule, and then you test your guess on every pair. A real detective always checks all the evidence. You should too!

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Getting Ready for Bigger Challenges

Once you are great at finding the rule in number pairs, you will be ready for even bigger puzzles! As you grow, the rules will get trickier. Here is what to expect.

What You Learn Now	What Comes Next
Add or subtract a small number (like +2 or −1)	Add or subtract bigger numbers (like +10 or −7)
One rule at a time	Two rules together (like add 1 then double)
Number pairs with two numbers	Number patterns with many numbers in a row

How number pair skills grow over time

The skills you build now are like building blocks. Every time you find a rule in a number pair, you are training your brain to think about patterns. Pattern thinking helps with all of math!

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Practice Problems

Now it's your turn! Try these problems. Remember to follow the detective steps: look, guess the rule, and check it!

Question 1: CONCEPTUAL

Look at this number pair: (2, 5). Did the number get bigger or smaller? Is the rule adding or subtracting?

Show answer

The number got bigger because 5 is more than 2. When a number gets bigger, the rule is adding. We can count up from 2 to 5: that is 3 jumps. So the rule is add 3. Always check: is the second number bigger or smaller? Bigger means add!

Question 2: BASIC CALCULATION

The number pairs are (1, 3) and (4, 6). What is the rule? Use the rule to find: (5, ?).

Show answer

Look at the first pair: 1 to 3 is counting up by 2. Now check the second pair: 4 to 6 is also counting up by 2. The rule is add 2. Now use the rule: 5 + 2 = 7. So the answer is (5, 7). Both pairs confirmed the rule before we used it.

Question 3: INTERMEDIATE

The number pairs are (7, 4) and (9, 6). What is the rule? Use the rule to find: (5, ?).

Show answer

Look at the first pair: 7 to 4. The number got smaller! Count down from 7 to 4: that is 3 jumps. The rule might be subtract 3. Check: 9 − 3 = 6. Yes! The rule is subtract 3. Now: 5 − 3 = 2. The answer is (5, 2). When the second number is smaller, think subtract!

Question 4: APPLIED

Sam has some bags of apples. When he starts with 2 apples, he ends with 6. When he starts with 3 apples, he ends with 7. What is Sam's rule? If Sam starts with 5 apples, how many will he end with?

Show answer

Let's find the rule. The first pair is (2, 6). Count from 2 to 6: that is 4 jumps, so the rule might be add 4. Check the second pair: 3 + 4 = 7. Yes! Now use the rule: 5 + 4 = 9. Sam will end with 9 apples. This is a real-life example of a number pair rule!

Question 5: CRITICAL THINKING

Look at these pairs: (1, 2), (2, 4), (3, 6). Someone says the rule is "add 1." Are they right? Why or why not? What is the real rule?

Show answer

Let's test "add 1." For (1, 2): 1 + 1 = 2. That works! But for (2, 4): 2 + 1 = 3, not 4. So "add 1" is wrong! It only worked for the first pair. The real rule is double the number (multiply by 2). Check: 1 × 2 = 2, 2 × 2 = 4, 3 × 2 = 6. All pairs work! This shows why you must always check every pair, not just one.

SUMMARY

What We Learned

Summary

A number pair is two numbers that are connected by a secret rule. Your job is to be a detective and find that rule! First, check if the second number is bigger (which means adding) or smaller (which means subtracting). Then count to find the exact number being added or taken away.

The most important step is to check your rule on every pair. If the rule works for all pairs, you found it! The main rules you will see are adding, subtracting, doubling, and staying the same. Keep practicing and you will become a number pair expert!